The Noise Model of the SEIS Seismometer of the InSight Mission to Mars

Abstract

The SEIS (Seismic Experiment for Interior Structures) instrument on board the InSight mission to Mars is the critical instrument for determining the interior structure of Mars, the current level of tectonic activity and the meteorite flux. Meeting the performance requirements of the SEIS instrument is vital to successfully achieve these mission objectives. The InSight noise model is a key tool for the InSight mission and SEIS instrument requirement setup. It will also be used for future operation planning. This paper presents the analyses made to build a model of the Martian seismic noise as measured by the SEIS seismometer, around the seismic bandwidth of the instrument (from 0.01 Hz to 1 Hz). It includes the instrument self-noise, but also the environment parameters that impact the measurements. We present the general approach for the model determination, the environment assumptions, and we analyze the major and minor contributors to the noise model.

Appendices

Appendix A: Minor Contributor Estimates

This section deals with minor contributors of the noise model.

1.1 A.1 Thermal Noise of the VBB Feedback Electronics

The VBB feedback electronics has its own sensitivity, and, as opposed to the VBB, is exposed only to the temperature profile inside the lander. There are requirements on the thermal sensitivity of the feedback (FB) electronics. The VBB POS output has a thermal sensitivity with respect to FB temperature less than $2\times 10^{-9}~\mbox{m}\,\mbox{s}^{-2}/\mbox{K}$ below 0.01 Hz and $5\times 10^{-8}~\mbox{m}\,\mbox{s}^{-2}/\mbox{K}$ over [0.01 0.1] Hz. The VBB VEL output shall have a thermal sensitivity with respect to FB temperature less than $5\times 10^{-9}~\mbox{m}\,\mbox{s}^{-1}/\mbox{K}$ over [0.01 0.1] Hz and $2\times 10^{-8}~\mbox{m}\,\mbox{s}^{-1}/\mbox{K}$ over [0.1 1] Hz. First the temperature profile within the E-box has been evaluated—see Fig. 36. Using the maximum thermal sensitivity, the thermal noise on the feedback electronics is calculated—see Fig. 37 and is found to be far below the L4 instrument noise requirement in both the horizontal and vertical directions.

Fig. 36

Left: e-box temperature prediction (Courtesy Lockheed Martin). Right: temperature spectrum calculated from the data and a linear model used in the noise calculations. This is a worst-case example

Fig. 37

Electronics feedback temperature noise—this noise is included in the VBB self-noise. The large extrapolation of the linear model from the measured data is justified assuming that the EBOX thermal behaviour is similar to a low pass filter

1.2 A.2 Buoyancy

The buoyancy noise derives from the seismometer design; in order to keep the VBBs in high vacuum, they are enclosed in an evacuated sphere. As the local atmospheric density varies in time, the Archimedes tensor will act upon the sphere, resulting in a vertical force exerted on the regolith. The displacement of the seismometer equilibrium caused by such air density variations results in an acceleration noise on the vertical axis of the seismometers.

Using the local atmospheric density as a function of time, $\rho (t)$, from the Mars Climate Database (Lewis et al., 1999), it is possible to estimate the buoyancy noise on the sphere. Similarly to Sect. 5.9, we have assumed that the ground behaves as an elastic half-space, that the SEIS feet are rigid and cylindrical in shape and that the force is equally distributed between each of the three SEIS feet. We use Hertzian contact mechanics to calculate the vertical displacement $x(t)$ of each foot as a function of time.

$$x(t) = \frac{1}{3}\frac{{F(t)}}{{2a{E^{*}}}} = \frac{1}{3}\frac{{mg - Vg\rho (t)}}{{2a{E^{*}}}} $$

where $V$ is the volume of the sphere, $m$ is the mass of SEIS, $g$ is the gravitational acceleration at the surface of Mars and a is the SEIS foot radius. $E^{*}$ is a function of the Poisson’s ratio and Young’s modulus of the ground and of the LVL feet (see B).

The vertical acceleration due to the density fluctuations is computed. Finally, the spectrum for this acceleration is calculated. We then compare this to the buoyancy noise derived from the Mars Path Finder pressure measurements (see Sect. 5.3). We assume that the Martian atmosphere is adiabatic and the atmospheric density variations can, therefore, be described by the following equation:

$$\rho (t) = {\rho _{0}}{\left( {\frac{{P(t)}}{{{P_{0}}}}} \right) ^{k}}$$

where $\rho (t)$ is the atmospheric density as a function of time, $\rho_{0}$ is the mean atmospheric density, $P(t)$ is the atmospheric pressure as a function of time, $P_{0}$ is the mean atmospheric pressure and $k$ is the adiabatic coefficient (1.28 for $\mathrm{CO}_{2}$).

Again we calculate the vertical displacement (or indentation depth) of each foot, the vertical velocity and acceleration as a function of time. The buoyancy noise level in the range of [0.01–1] Hz is calculated to be ${<}10^{ - 11}~\mbox{m}/\mbox{s}^{2}/\sqrt{\mbox{Hz}}$.

1.3 A.3 Noise Due to Dust Impact on the WTS

As SEIS is not buried but rather is deployed on the Martian surface, another potential noise resulting from the wind is the vibrations due to the aggregate mass of multiples, wind blown saltating sand particles on SEIS that may impact the Wind and Thermal Shield (WTS). The design of the WTS has been specifically tailored to minimize this impact: a weighted ${\approx} 10~\mbox{cm}$ high fabric skirt (reinforced by chainmail) provides both closure to inside the WTS and mechanical damping of dust effects on the WTS rigid structure.

Due to the geometry of the WTS (a cone section of ${\sim} 30~\mbox{cm}$ diameter and ${\sim} 30~\mbox{cm}$ height), we have assumed two kinds of effects:

– A direct impact coming from micron-size particles from the suspended dust in the wind flux (their quantity being estimated by opacity measurements): the acceleration on the WTS is proportional to the maximum wind spectrum. The effect can be scaled from the wind effect on the WTS, by estimating the mass load of the incoming wind, corrected by the dust loading mass. This effect is negligible: as a matter of fact, the dust loading for an entire column of Mars atmosphere during a dust storm is estimated to about $4~\mbox{g}/\mbox{cm}^{2}$ Martin (1995). Spread over the entire air column, this is to compare with the typical Mars atmospheric density ($0.02~\mbox{kg}/\mbox{m}^{3}$): it turns out that the contribution of dust loading is small with respect to the daily atmospheric density variations (0.0155 to $0.0220~\mbox{kg}/\mbox{m}^{3}$).

– A secondary impact coming from “saltation particles” flux from saltation models Kok (2010): these heavier particles have mostly a ballistic trajectory and impact the WTS with a ≈45 deg angle. The saltation is initiated when the shear stress exerted by wind on the soil surface exceeds the fluid threshold Kok (2010), at which point surface particles are lifted Kok et al. (2012). These lifted particles undergo ballistic trajectories during which they are accelerated by wind drag. It is also worth pointing out that there is a low velocity zone at the leading surface of the WTS, and as the impact moves more to the side, the impact becomes more and more oblique.

However, in this last case, the saltation process is very unsteady. As underlined in Kok et al. (2012), as well as in Stout and Zobeck (1997), the saltation process depends on a threshold value of the shear stress near the surface Kok and Renno (2009). Therefore, this saltation effect is limited to a reduced period of time, when the wind velocity is over a threshold $u^{\star }$. Following Kok (2010), the minimum wind shear speed ($u^{\star }$) for saltation is about 0.5 m/s (for $100~\upmu \mbox{m}$ grains). We can estimate the wind shear speed from the wind speed at one measurement location, $U_{x}(z)$, if we make an assumption on the surface roughness, $z_{o}$:

$${u^{\star }}=\kappa Ux( z ) /\mbox{ln}(z/z_{o}). $$

Here, we use the in-situ wind measurements from Phoenix, Viking Lander 1 and Viking Lander 2 to estimate the shear velocity statistics assuming a surface roughness (for the InSight landing site, $z_{o}\approx 3~\mbox{cm}$). The influence of the surface roughness on the shear wind speed statistics is also investigated (shear wind speed increases with surface roughness; see Fig. 38). For most of the measured wind speeds, the shear wind speed stays below the threshold.

Fig. 38

Combined shear velocity statistics: even in the surface roughness worst case (5 cm), the wind shear velocity is below 1 m/s $90\%$ of the time

The shear wind variability has also been estimated, as a function of the local time on the basis of the in-situ wind measurements (Fig. 38). For most of the time, even small particles (100 μm grains) are not uplifted (see Fig. 39). Though there are instances in which it may be significant, we can conclude that saltation noise will be triggered by very specific wind conditions: it is expected to occur during “bad weather” periods, excluded from our typical $1 \sigma$ statistics.

Fig. 39

Combined mean shear velocity vs local time, compared to 100 μm wind speed saltation threshold

1.4 A.4 Electric field impact

Even if no electric field has been recorded yet on Mars (ExoMars 2016 will carry an electric field measurement experiment described in Déprez et al. 2015), there are several possible physical phenomena that could generate one, ranging from electrostatic charging to possible thunderstorms—see Melnik and Parrot (1998). Among these processes, the saltation process and the transport of wind-blown sand, as well as dust storms and dust devils can produce local electric fields at the surface of Mars, see Kok and Renno (2008). Even if SEIS’ sensitivity to external electric fields is minimized by the grounding scheme of the instrument, the tether is sensitive to the variations of the electric field and therefore SEIS measurement could in principle be influenced by such phenomena.

Similarly to the temperature and magnetic field noise determination, the electric field noise is estimated in several steps. First, an experimental tether sensitivity to the electric field is estimated. Next, an estimate is made of the electric fields that are likely to be found at the surface of Mars. Finally, these are combined to determine the electric field noise on SEIS.

The E-field noise has been modeled as an additional voltage noise that comes into the VBB feedback loop at the integrator level. From the VBB feedback loop design, the transfer function between the VBB outputs and a noise added at integrator level is well known (it is an acceleration divided by Volt quantity depending on the frequency). Tests were performed in order to determine the worst case susceptibility of one meter of tether to the E-field (Tether E-field sensitivity CNES report, Schandler et al., 2015). Assuming a tether with a 70 cm vertical component and 3 m flat/horizontal component (similar to the flight model) the sensitivity is extrapolated to be 4 μV/kV/m.

If grain transport occurs, there is an electric field that develops at the surface of Mars. The electric field generated as a function of the saltation mass flux is presented in Fig. 40. However, if there is no grain transport, there is no electric field and thus no electric field noise on SEIS. From the previous section, which analyzes the conditions for saltation initiation on InSight landing site, we can conclude that perturbation by in-situ electric fields will also be triggered by very specific wind conditions (storm, dust devils, …). Such conditions are already included in the fraction of the time (“bad weather”) where the performance is already strongly degraded by environmental conditions.

Fig. 40

Electric field generated as a function of the saltation mass flux (private communication, Kok, 2015)

Appendix B: Summary of Environment Assumptions

This appendix is a summary of the environment assumptions.

(See Fig. 41 for a summary of the chosen approach.)

Fig. 41

Summary of the environment assumptions

2.1 B.5 Temperature Assumptions

Martian temperature spectra used (see Figs. 42, 43) are derived from Mars PathFinder and Viking data. Two types of datasets are derived from these data. A first “short term” dataset is used for the noise analysis. As a matter of fact, if we are interested in the seismic bandwidth (and its daily variation) for the noise model, the peak-to-peak temperature excursion is also important, in order to assess potential saturation issues on the VBB sensors. PathFinder measurements have been recorded at higher frequency, and Viking measurements have a lower frequency, but are ranging over a longer time span, including seasonal variations.

Fig. 42

Viking Lander temperature model and seasonal means. (a) The Viking Lander 1 and (b) the Viking Lander 2 temperature data with bad data removed (black), the temperature model (cyan) and the seasonal mean (red line)

Fig. 43

Mars Pathfinder temperature data and spectrum. (a) Mars Pathfinder atmospheric temperature at the height of the bottom-mast thermocouple (sequence 1030 from sol 25) as a function of time. (b) Spectra of the VL1 (blue), VL2 (green) and MPF temperature data (red)

For the “short period” spectrum, we are mostly using Mars Path Finder data from a period of approximately 10 sols (sols 18–27 of the mission; data obtained from the Planetary Data Server). These data are chosen as they span several sols and have a sampling rate high enough to be compatible with our bandwidth requirements. Temperature data are first corrected for both the seasonal climate variations and the daily harmonics, leaving the residual temperature variations, from which the temperature residuals that the spectra are calculated. The linear models then correspond approximately to the mean, $1 \sigma$ and $3 \sigma$ spline fits of the spectra of the residuals at low frequencies. They are then separated into a “day” and “night” spectra based on the local hour of the data used to generate the spectrum. A “day” spectrum is entirely within the day period, a “night” spectrum is entirely within the night period. The daytime period was chosen arbitrarily to be from 6 am to 6 pm (night is from 6 pm to” 6 am).

At longer periods Viking data are used. First, places where the Viking Lander sampling was interrupted (i.e., the time between two samples is much larger than the normal time between samples) and missing temperature data points are thus identified in the raw Viking Lander data. Periods when either the sampling was interrupted for too long (more than 40 sols) or too many consecutive data points were missing in the raw data for the data to be meaningful were removed the data set. The remaining bad temperature data points (indicated by a temperature of −273.15 C) were replaced with the mean temperature over the entire data set. It is necessary to remove the daily and seasonal temperature variations in order to remove the harmonics in the final temperature spectrum. To do this a temperature model is derived taking into account the seasonal climate variations and the daily harmonics.

In order to simply the analysis, linear temperature models are derived from the data (Fig. 45). The temperature models are defined as a function of frequency $(f)$ with amplitude (A) and cut-off frequency $f_{\mathit{cut}}$ of ${\sim} 0.1~\mbox{Hz}$ i.e.:

$$f < {f_{\mathit{cut}}}:{T_{m}}\left( f \right) = A\sqrt{\frac{{{f_{\mathit{cut}}}}}{f}} $$

and

$$f \geqslant {f_{\mathit{cut}}}:{T_{m}}\left( f \right) = A\frac{{{f_{\mathit{cut}}}}}{f} $$

For both the day and night spectra, we define a ${\sim} 1 \sigma$ model, a ${\sim} 3 \sigma$ model and a mean model. The amplitudes of these linear models are determined by calculating a mean spectrum (using a spline fit) and the standard deviation ($1 \sigma$) of the mean spectrum. As the data cannot be fit perfectly by the linear model, we assume conservative amplitudes (particularly during the day time and within the SEIS bandwidth). The amplitudes of the linear temperature models are given in the Table 44:

Fig. 44

Linear temperature model amplitudes

Fig. 45

Temperature statistics derived from Mars Pathfinder data. Day related data (in red) are significantly higher than night data (in blue). Simplified spectra corresponding to mean, $1\sigma$ and $3\sigma$ fit are presented, in green for night time and yellow for day time, respectively in dashed, dot-dashed and plain lines. The data are consistent with long-period data from the Viking missions

2.2 B.6 Summary of Ground Properties

Two types of laboratory tests have measured regolith properties using a Martian regolith simulant: seismic velocity tests and axial response tests. In the complete InSight seismic noise model presented here, the seismic velocity measurements are extrapolated to the Martian environment. The three ground stiffness predicted for under the three SEIS feet on Mars (Fig. 46) are consistent with results from Delage et al. (2017).

Fig. 46

Soil stiffness summary of measurements. CERMES experiments refer to Delage et al. (2017)

2.3 B.7 Wind Assumptions

Martian wind speed squared spectra are derived from Phoenix data, VL1 and VL2 data (Figs. 47, 48). The form of the linear models comes from the data at low frequencies, and from theoretical arguments at high frequencies. The amplitudes of the flat section of the linear models correspond approximately to the mean, $1\sigma$ and $3\sigma$ amplitudes of the wind speed squared spectra at 15 mHz (the estimated cut-off frequency between two regimes). When determining the wind speed at different heights, the complete InSight seismic noise model presented here assumes that the surface roughness length on Mars is 3 cm. See Murdoch et al. (2016b) for more details of the wind analyses.

Fig. 47

Wind statistics used in the noise model

Fig. 48

In order to be as close as possible from the ground truth, we have chosen to use Viking Lander 2 wind statistics in the ISAE SEIS noise model

2.4 B.8 Pressure Tilt Assumptions

The pressure noise is a ground tilt induced by pressure fluctuations caused by the wind. A pressure and wind field has been generated around the landing site thanks to a LES simulation as described in Spiga and Forget (2009). The resulting pressure noise tilt (vertical and horizontal) is estimated at two wind speeds by Sorrels method (see Fig. 49). An extensive description of the methods is provided in Murdoch et al. (2016a) and Kenda et al. (2016). Our noise model extrapolates from these values for intermediate wind speeds.

Fig. 49

Reference pressure tilt for two typical wind speed assumptions 3.5 m/s and 8 m/s—data from Lognonné et al. (2016)—LES simulations at landing site from Spiga et al. (2012), private communication

2.5 B.9 Magnetic Field assumptions

No magnetic data have ever been recorded at the surface of Mars. Therefore, the magnetic field at the surface (see Fig. 50) is estimated using in-orbit measurements (e.g. Langlais et al. 2004) extrapolated with new data (Johnson et al., 2016, private communication). Several MGS tracks from 2003 and 2006 have been used to retrieve the crustal magnetic field variations. These measurements have been corrected for spatial variations (motion of the satellite) and show only external field variations. The linear model is based on the $70\%$ (${\sim} 1\sigma$) spectrum.

Fig. 50

Magnetic field assumptions—data from Johnson et al., (2016), private communication

2.6 B.10 Gravity Assumptions

There are only small variations in the gravity field on the surface of Mars in the InSight landing site. A value of $3.71~\mbox{m}/\mbox{s}^{2}$ is always used in the ISAE SEIS noise model (see Fig. 51). The model used is described in Hirt et al. (2012).

Fig. 51

Gravity field assumptions—data from Hirt et al. (2012)

Appendix C: Other Noise Model Parameters of Interest

In Table 6 are described the key hardware parameters used in the noise model. These are the best current estimates at the time of publication. For more details about the mechanical noise (lander, WTS, HP3) parameters, the reader is referred to Murdoch et al. (2016b).

Table 6 InSight seismic noise model key hardware parameter assumptions—current best estimates at the time of publication